Device for determining the amplitude of the spectral lines in the output signal from a ring interferometer

ABSTRACT

An arrangement for determining the amplitudes of spectral lines contained in the phase-modulated output signal of an optical ring interferometer which are suited to determine the angular velocity with which the ring interferometer is rotated, for which a digital evaluation circuit is utilized. Two light waves moving in opposite directions in a fiber optical wave guide are analyzed upon exiting the wave guide. The light waves exiting at one end of the fiber optic wave guide are phase-modulated in order to obtain an output signal of the fiber ring interferometer suitable for determining the Sagnac phase.

The present invention relates to an arrangement for determining theamplitudes of spectral lines contained in the phase-modulated outputsignal of an optical ring interferometer which are suited to determinethe angular velocity with which the ring interferometer is rotated, forwhich a digital evaluation circuit is utilized.

Such a method is disclosed in DE 31 40 110 A1. Two light waves moving inopposite directions are propagated in the fiber-optical wave guide,forming a ring-shaped light path, of the ring interferometer andinterfere with each other when they exit. The interference is a functionof the angular velocity with which the fiber-optical wave guide, whichforms at least one coil, is rotated. The phase difference between thetwo light waves which have travelled through the fiber-optical waveguide in opposite directions is proportional to the angular velocity. Ascan be gathered from DE 31 40 110 A1, this phase difference, which iscalled a Sagnac phase, can be determined from the amplitudes of thespectral lines of the interference light exiting the fiber-optical waveguide.

The light waves exiting at one end from the fiber-optical wave guide arephase-modulated in order to obtain an output signal of the fiber ringinterferometer suitable for determining the Sagnac phase. Evaluation ofthe analog output signal is advantageously performed by means of digitalsignal processing to determine the Sagnac phase. Since the analog outputsignal has a disadvantageously high frequency level for subsequentdigital signal processing because of the required high phase modulationfrequency, according to DE 31 40 110 A2 either the output of the lightfed into the fiber ring interferometer is pulsed with a suitablefrequency or the output signal is reduced by means of a mixer to a lowerfrequency level. Both solutions involve additional circuit expenditures.A further disadvantage of the mixing process is that undesired mixingproducts are created which must be suppressed by additional analogfiltering so that the scanning theorem is satisfied and therefore noimpermissible spectral convolution products are created which wouldgreatly distort the signal to be evaluated.

It is therefore the object of the invention to recite an arrangement ofthe previously mentioned type which determines, with a small technicalexpenditure in circuits, as exactly as possible the amplitudes ofdesired spectral lines from the output signal of a ring interferometer.

The above and other objects are achieved, according to the presentinvention, in a digital evaluation circuit for determining theamplitudes of spectral lines contained in a digitized phase-modulatedoutput signal of an optical ring interferometer which is being rotated,wherein the spectral lines contain information indicating the angularvelocity with which the ring interferometer is being utilized, by theimprovement wherein the circuit comprises: a frequency-selective filterconnected for splitting the digitized output signal of the ringinterferometer into first and second signal portions, the first signalportion containing spectral lines corresponding to odd-numberedmultiples of a given frequency which is one of the phase modulationfrequency and a frequency derived from the phase modulation frequencyand the second signal portion containing spectral lines corresponding toeven-numbered multiples of the given frequency, wherein the spectrallines contained in the first and second signal portions are available byselective frequency separation; and two digital filters each connectedto receive a respective signal portion and to filter out of therespective signal portion a signal element at the frequency of oneselected spectral line in order to allow determination of the amplitudeof the filtered spectral line.

Advantageous embodiments and features of the invention will be describedbelow.

Because of the employment of a frequency-selective filter in accordancewith the invention, no great demands need to be made on the subsequentdigital filters in respect to their selection.

The invention will be described in detail below by means of severalexemplary embodiments illustrated in the drawings. Shown are in:

FIG. 1 a block diagram of a circuit for determining the amplitudes ofcertain spectral lines from the output signal of a ring interferometer,

FIG. 2 a frequency-selective filter of this circuit,

FIG. 3 several frequency spectra,

FIG. 4 a first embodiment,

FIG. 5 a second embodiment, and

FIG. 6 a third embodiment of a complex digital filter.

The output signal of a ring interferometer is known (see DE 31 40 110A1) to have the following form: ##EQU1## Here, the factors J_(n) (2ψ)with n=0, 1, 2, . . . are the values of the 1st order Bessel functionfor the argument 2ψ=2ψ_(o) sin πf_(m) τ. I_(o) indicates the intensityof the light fed to the ring interferometer, ψ_(o) the modulation indexof the phase modulation performed with the frequency f_(m) and τ thetravel time of the light waves through the ring interferometer. Theso-called Sagnac phase is indicated by φ, which is proportional to theangular velocity with which the ring interferometer is being turned.This Sagnac phase φ is to be determined in the end. It can be calculatedfrom the amplitudes of three or four spectral lines of the output signali(t). The amplitudes A1 to A4 of, for example four spectral lines, whichare functions of the Sagnac phase are listed below:

    A1=2I.sub.o J.sub.1 (2ψ) |sin2φ|

    A2=2I.sub.o J.sub.2 (2ψ) cos2φ

    A3=2I.sub.o J.sub.3 (2ψ) |sin2φ|

    A4=2I.sub.o J.sub.4 (2ψ) cos2φ

A circuit is shown in FIG. 1, by means of which the four spectral lineamplitudes A1 to A4 can be determined. The analog output signal i(t) ofa ring interferometer IP first is digitized in an analog-digitalconverter AD and is then supplied to a frequency-selective filter FW,which splits the digitized output signal into two signal portions s1 ands2. The first signal portion s1 contains all spectral lines of theoutput signal i(t) [see equation (1)] with the odd-numbered multiples ofthe phase modulation frequency f_(m) (or of a frequency derivedtherefrom), i.e. all spectral lines the amplitudes of which arefunctions of sin 2φ. The second signal portion s2 contains all spectrallines with the even-numbered multiples of the phase modulation frequencyf_(m) (or of a frequency derived therefrom), i.e. all spectral lines theamplitudes of which are functions of cos2φ. FIG. 3 illustrates thesplitting of the output signal i(t) with the spectral lines nf_(m) (n=1,2, 3, . . . ) into the first signal portion s1, which only contains thespectral lines with the odd-numbered multiples of the phase modulationfrequency f_(m), and into the second signal portion, which only containsthe even-numbered multiples of the phase modulation frequency f_(m). Apre-selection of the spectral lines takes place by means of this splitof the output signal i(t) into the two signal portions s1 and s2, whichhas the advantageous consequence that the distances between the spectrallines appearing in each signal portion are twice as large as thedistances between the spectral lines of the original output signal. Forthis reason the selection of the individual signal portions s1 and s2can be performed with less expensive, i.e. less selective filters.

Each signal portion s1, s2 is supplied to two parallel filter branches,which determine the spectral line amplitudes A1 and A3, which arefunctions of sin2φ, from the first signal portion s1, and from thesecond signal portion s2 the spectral line amplitudes A2 and A4, whichare functions of cos2φ. A mixing arrangement M is contained in eachfilter branch, which nominally reduces a respective spectral line fromthe signal portion s1 or s2 supplied to it to the frequency zero and inthe course of this changes the originally real signal into a complexsignal. For this purpose, each mixing arrangement M is charged with acomplex scanned carrier signal of the form

    e.sup.-j2πf.sbsp.cl.sup.k/f.sbsp.A/                     (3)

where f_(cl) =lf_(m) (with l=1, 2, 3, 4), f_(A) is the scanningfrequency of the respective signal portion s1 or s2, and k=1, 2, 3 . . .(time index). Following the mixing arrangement M is a complex lowbandpass filter F1, with which possibly a further complex low bandpassfilter F2 is connected in series. After the frequency-selective filterFW already has lowered the scanning frequency of the digitized outputsignal, the scanning frequency is further reduced in each filter F1, F2,so that it has an advantageous lower value for the digital processing ofthe spectral line amplitudes A1 to A4. Because of the fact that eachspectral line which is to be selected in a filter branch is nominallyconverted to frequency zero, it is possible to use identical complexdigital low bandpass filters F1 or F2 in all filter branches.

The respectively filtered-out spectral line, split into a real and animaginary portion, is available at the output of each complex digitallow bandpass filter F1, F2. Its amplitude A1, A2, A3, A4 can bedetermined in a known manner by squaring the real and the imaginaryportions, their addition and subsequent root formation. This operationis performed by a circuit block B. The circuit blocks M, F1, F2 whichprocess complex signals are shown by double lines in FIG. 1.

The Sagnac phase φ is calculated from the detected spectral lineamplitudes A1 to A4 in a processor P. How to derive the Sagnac phase φfrom four spectral line amplitudes is disclosed in the older Germanpatent application P 39 35 357. The older German patent application P 3941 991 proposes a method in accordance with which the Sagnac phase φ canbe determined from three spectral line amplitudes. In accordance withthe latter, only three filter branches are required.

In accordance with FIG. 2, the frequency-selective filter FW is embodiedas a comb filter in which the transmission bands and the stop bandsiteratively alternate periodically equidistant in the frequency rangefrom 0 to f_(A) (scanning frequency of the analog-digital converter AD).

It is assumed that f_(A) =p·f_(m), where p/2 is a whole, odd number. Incase p=10, i.e. where the scanning frequency f_(A) of the digitizedoutput signal of the ring interferometer corresponds to ten times thephase modulation frequency f_(m), the delay rates (10 T, 4 T withT=1/f_(A)) and coefficients (1/8, 3/8) should be selected in the combfilter as indicated in FIG. 2. Because of the reversal at the inputbetween the circuit paths 0 and 1 with the scanning frequency f_(A), thescanning frequency f_(A), of the two signal portions s1 and s2 isreduced to f_(A),=1/2 f_(A) at the output of the comb filter. In thisfrequency-selective filter embodied as a comb filter, the two signalportions s1 and s2 are always given the same value, i.e. even errorshave the identical effect on both signal portions. Because of this thereare no distortions generated when determining the Sagnac phase φ,because the Sagnac phase is calculated from the signal portions s1 ands2 by forming the quotient of the amplitudes (see P 39 35 357).

The complex mixing arrangement M and the complex low bandpass filter F1connected downstream of it which in accordance with FIG. 1 are presentin each filter branch can, as shown in FIG. 4, be realized by means oftwo real mixers M1 and two downstream connected identical, digital (forexample transverse) low bandpass filters F11 with real components. Thelow bandpass filters F1 best reduce the scanning frequency f_(A), of theoutput frequency of the frequency-selective filter FW by the factor p/2,i.e. by the factor 5. The respective signal portion s1 or s2 with thecarrier cos ω₁, provided by the frequency-selective filter FW, is mixeddown to the frequency F=0 in one of the two mixers M1. The mixingproduct generated in the course of this represents the real portion ofthe signal portion. The associated imaginary portion is generated bymeans of the mixing process of the signal portion s1 or s2 with thecarrier sin ω₁ in the other mixer M1. The two carrier signals cos ω₁ andsin ω₁ have the argument ω₁ =2πf_(cl) k/f_(A'). This type of complexfiltering is described by M. Bellanger in his book "Digital Processingof Signals", 2nd. Edition, John Wiley & Sons, publ., pages 356 and 357.

The combination of a complex mixing arrangement M and a complex filterF1 present in each filter branch in accordance with FIG. 1 can also berealized by means of a transverse digital filter with complexcoefficients. Such a filter can be seen in FIG. 5, which consists, forexample, of five (=p/2) signal paths 0 . . . 4, to which the scanningvalues of the signal portion s1 or s2 provided by thefrequency-selective filter FW are cyclically switched. This switchingprocess reduces the scanning frequency f_(A), of the respective signalportion s1 or s2 by the factor p/2=5, the same as the originalarrangement. The real and imaginary coefficients required for the filterhave been entered in FIG. 5. A first adder AD1 at the output of thefilter circuit adds all real signal components from the five signalpaths, and the imaginary signal components are combined by a secondadder AD2.

A further variant of a filter arrangement, which filters out aparticular spectral line from the real signal portion s1 or s2 providedby the frequency-selective filter FW and converts it into a complexsignal with a scanning frequency reduced by the factor p/2 (=5), can beseen in FIG. 6. This filter arrangement consists of a decimation filterDZF (on the left side of the dashed line) embodied as a polyphasenetwork with real coefficients C1 . . . C5, in which the scanningfrequency is reduced by the factor p/2=5 by means of a switchingprocess, as in the filter of FIG. 5. A network DFT follows thedecimation filter DZF, which splits the spectral line separated by thedecimation filter DZF into a real and an imaginary signal by means of adiscrete Fourier transformation.

The coefficients required for the network DFT have been entered intoFIG. 6. A first adder AD3 at the output of the network DFT combines thereal signal components, and a second adder adds the imaginary signalcomponents.

A further advantage in regard to efforts of the arrangement inaccordance with FIG. 6 is that only one decimation filter DZF isrequired for each signal portion s1 or s2 (i.e. a total of 2DZF), andthat only one discrete network DFT must be provided for the individualamplitudes.

I claim:
 1. In a digital evaluation circuit for determining amplitudesof spectral lines contained in a digitized phase-modulated output signalof an optical ring interferometer which is being rotated, wherein thespectral lines contain information indicating the angular velocity withwhich the ring interferometer is being utilized, the improvement whereinsaid circuit comprises: a frequency-selective filter connected forsplitting a digitized output signal of the ring interferometer intofirst and second signal portions, the first signal portion containingspectral lines corresponding to odd-numbered multiples of a givenfrequency which is one of the phase modulation frequency and a frequencyderived from the phase modulation frequency and the second signalportion containing spectral lines corresponding to even-numberedmultiples of the given frequency, wherein the spectral lines containedin the first and second signal portions are available by selectivefrequency separation; and two digital filters each connected to receivea respective signal portion and to filter out of the respective signalportion a signal element at the frequency of one selected spectral linein order to allow determination of the amplitude of the filteredspectral line.
 2. An arrangement in accordance with claim 1, whereinsaid digital filters are complex filters, and each said complex filtersplits a signal element into a real signal component and an imaginarysignal component, with which said circuit can determine the amplitude ofthe filtered out spectral lines from the real and imaginary componentsby quantification.
 3. An arrangement in accordance with claim 2, whereinsaid digital filters are low bandpass filters which filter the signalelements out of frequency ranges containing the selected spectral linesafter the selected spectral lines have been mixed down to a very lowfrequency level.
 4. An arrangement in accordance with claim 1, whereinsaid digital filters are low bandpass filters which filter the signalelements out of frequency ranges containing the selected spectral linesafter the selected spectral lines have been mixed down to a very lowfrequency level.
 5. An arrangement in accordance with claim 1, whereinthe frequency-selective filter is a comb filter.
 6. An arrangement inaccordance with claim 4, wherein the ring interferometer produces ananalog phase-modulated output signal and the digitized phase-modulatedoutput signal is formed by sampling the analog signal at a samplingfrequency, and said frequency-selective filter halves the samplingfrequency of the digitized output signal of the ring interferometer. 7.An arrangement in accordance with claim 1, wherein the ringinterferometer produces an analog phase-modulated output signal and thedigitized phase-modulated output signal is formed by sampling the analogsignal at a sampling frequency, and said frequency-selective filterhalves the sampling frequency of the digitized output signal of the ringinterferometer.
 8. An arrangement in accordance with claim 7, whereinsaid digital filters further reduce the sampling frequency of the signalportions emitted by said frequency-selective filter.
 9. An arrangementin accordance with claim 1, wherein the ring interferometer produces ananalog phase-modulated output signal and the digitized phase-modulatedoutput signal is formed by sampling the analog signal at a samplingfrequency, and each digital filter comprises a plurality of complexfilters connected together in cascade and each being operative to reducethe sampling frequency of the signal supplied to it.
 10. An arrangementin accordance with claim 9, wherein said digital filters are complexfilters, and each said complex filter splits a signal element into areal signal component and an imaginary signal component, with which saidcircuit can determine the amplitude of the filtered out spectral linesfrom the real and imaginary components by quantification.
 11. Anarrangement in accordance with claim 9, wherein said digital filters arelow bandpass filters which filter the signal elements out of frequencyranges containing the selected spectral lines after the selectedspectral lines have been mixed down to a very low frequency level. 12.An arrangement in accordance with claim 1, wherein the ringinterferometer produces an analog phase-modulated output signal and thedigitized phase-modulated output signal is formed by sampling the analogsignal at a sampling frequency, and each of said digital filters is atransverse filter with complex coefficients which generates complexoutput signals with a reduced sampling frequency from a real signalprovided by said frequency-selective filter.
 13. An arrangement inaccordance with claim 12, wherein said digital filters are complexfilters, and each said complex filter splits a signal element into areal signal component and an imaginary signal component, with which saidcircuit can determine the amplitude of the filtered out spectral linesfrom the real and imaginary components by quantification.
 14. Anarrangement in accordance with claim 12, wherein said digital filtersare low bandpass filters which filter the signal elements out offrequency ranges containing the selected spectral lines after theselected spectral lines have been mixed down to a very low frequencylevel.
 15. An arrangement as defined in claim 1, wherein the ringinterferometer produces an analog phase-modulated output signal and thedigitized phase-modulated output signal is formed by sampling the analogsignal at a sampling frequency, and each said digital filter comprises:a polyphase filter operative to reduce the sampling frequency of therespective signal portion and to produce a real filtered signal; and anetwork connected to perform discrete Fourier transformation on thesignal produced by said polyphase filter and to split the real signalinto a real signal component and an imaginary signal component.
 16. Anarrangement in accordance with claim 1, wherein the ring interferometerproduces an analog phase-modulated output signal and the digitizedphase-modulated output signal is formed by sampling the analog signal ata sampling frequency, and the sampling frequency of the digitized outputsignal of the ring interferometer is equal to p times the givenfrequency, where p/2 is an odd integer.
 17. An arrangement in accordancewith claim 16, wherein said digital filters are complex filters, andeach said complex filter splits a signal element into a real signalcomponent and an imaginary signal component, with which said circuit candetermine the amplitude of the filtered out spectral lines from the realand imaginary components by quantification.
 18. An arrangement inaccordance with claim 16, wherein said digital filters are low bandpassfilters which filter the signal elements out of frequency rangescontaining the selected spectral lines after the selected spectral lineshave been mixed down to a very low frequency level.